Very often scientific data are defined by multidimensional vectors of numerical values. To enable exploratory data analysis involving heuristic abilities of human experts visualization of data is highly desirable: picture is worth a thousand words. There are different approaches to visualization. We consider one of the most popular approaches known as multidimensional scaling. By means of multidimensional scaling a set of multidimensional vectors can be represented as a set of points in a low-dimensional space, and exposed in this way to a human expert for heuristic analysis. Even more general sets of objects can be visualized: it is sufficient to know pairwise similarity/dissimilarity between the objects. An essential part of this technique is optimization of a function possessing many optimization adverse properties as non-differentiability, multimodality, invariants. The objective function is defined by an analytical formula, which may seem rather simple, but its minimization is a difficult global optimization problem. Although improved local search procedures are used for some applications of multidimensional scaling certain applications can be solved only with global optimization. In this talk global optimization algorithms for multidimensional scaling are reviewed showing when global optimality may be guaranteed.